Question 32
Let $ABC$ be an acute triangle, with incircle $\omega$ of centre $I$ and circumcircle $\Omega$ of centre $O$. Let $M$ be the midpoint of altitude $AH$, where $H\in BC$. The circle $\omega$ touches $BC$ at $D$. Line $MD$ meets $\omega$ again at $P$, and the perpendicular from $I$ to $MD$ meets $BC$ at $N$. Lines $NR,NS$ are tangent to $\Omega$ at $R,S$, respectively. Prove that $R,P,D,S$ are concyclic.